Simplifying+Expressions

When a mathematical expression is simplified, an equivalent expression is found that is simpler than the original. This means that the simplified expression is smaller that the original. There is no exact procedure for simplifying all algebraic expressions because there are so many different kinds of expressions.But in order to simplify mathematical expressions you will be required to follow certain steps.
 * __Simplifying Expressions__** means writing the expression in the most compact or efficient matter.

Fractions Exponents Combining like terms Properties Factoring Order of Operations Adding, Subtracting, Multiplying or Dividing Positive and Negative integer
 * __The different kinds are:__**
 * Distributive Property
 * Associative Property
 * Commutative Property

Fractions may be the easiest mathematical expressions to simplify. There are no hard steps. just a few steps to follow. Fractions may have numerators and denominators that are composite numbers (numbers that has more factors than 1 and itself).
 * __Simplifying Fractions:__**

__How to simplify a fraction:__
 * The first thing you do is to find a common factor of the numerator and denominator. A common factor is a number that will divide into both numbers evenly. Two is a common factor of 4 and 14.
 * Next you divide both the numerator and denominator by the common factor.
 * Then repeat this process until there are no more common factors.
 * And then the fraction is simplified when no more common factors exist.

__An example of simplifying fractions:__ 12/18, the first thing you do is to list the common factors. The common factors of 12 and 18 are 1, 2, 3, and 6. From this list you choose the greatest common factor which is 6. You then divide the numerator and the denominator by 6. And you get a simpler form of the fraction which will be 2/3. And thats the simplest form of 12/18.

Exponents might be easy for some kids while it might be difficult for others. To simplify exponents you will have to follow some steps. To simplify an expression with exponents, first simplify each term according to addition, subtraction multiplication, division, distribution, and power to power rules. Then, combine like terms and arrange the terms, putting those with variables first, in order of highest exponent.
 * __Simplifying Exponents:__**

__An example of simplifying exponents:__ math (x^2+2x^2)^5 -(3x^3)(4x^4)+(11x)^2 math

(//x//^2 +2//x//^2)^5 - (3//x//^3)(4//x^//4) + (11//x//)^2

You first combine like terms. = (3//x//^2)^5 - (3)(4)//x^//3+4 +112//x//^2

You then do the multiplication, in other words do the calculate in the parenthesis = 35//x//^2(5) -12//x//^7 +121//x^//2

You then follow the exponents and get your final answer. = 243//x//^10 - 12//x//^7 +121//x//

Combining like terms is another way to simplify mathematical expressions. Combining like terms is a process used to simplify an expression or an equation using addition and subtraction of the coefficients of terms. You can add, subtract, multiply or even divide to combine any like terms.
 * __Combining Like Terms:__**

__An example of combing like terms:__ 5x^2 + 7x + 2 - 2x^2 + 7 + x^2

The first thing you do is look carefully at the expression and try to see if there are any like terms. We identify sets of like terms. Both 2 and 7 are like terms because they are both constants. The terms 5x^2, -2x^2, and x^2 are like terms because they each consist of a constant times x squared. Then you look at the left overs, 2 and 7. Since there is an addition sign, you add them. So 2+7 is 9. The coefficients of the second set of like terms are 5, -2, and 1. Therefore, when added the result is 4. So after combing all the like terms, the final expression looks like this: 9 + 7x + 4x^2

__**Properties:**__ While simplifying mathematical expressions you would definitely come across the three different properties. The first property is called the distributive property. Distributive property, is used to multiply a single term and two or more terms inside a set of parentheses. The second property is called the commutative property. Commutative Property can be used for addition and multiplication. That is, a + b = b + a. That is, a × b = b × a. The third property is called the associative property. Associative Property is like Commutative Property but just a little different. In Commutative Property you only deal with two set of numbers, but in Associative Property you will have to deal with more than two numbers.
 * Commutative Property of Addition: It states that changing the order of addends does not change the sum.
 * Commutative Property of Multiplication: It states that changing the order of factors does not change the product.